Here \(\displaystyle \texttt {SODM}\)  is the equation of the sextic \(\displaystyle \mathrm {S_{ODM}}\) , \(\displaystyle \texttt {P}\)  is \(\displaystyle \mathrm {Det}_{\mathbb {O}}\) , \(\displaystyle \texttt {PHI123}\)  is \(\displaystyle \phi (c,b,a)\)  and \(\displaystyle \texttt {ASS123square}\)  is \(\displaystyle  \bigg |[c,b,a] \bigg |^2\) . We have used the formula (see lemma 6.56 and 6.61 in [1]}):
\( \bigg |[c,b,a] \bigg |^2 = 4 \bigg (\mathrm {Gram}(\mathrm {Im}(c),\mathrm {Im}(b), \mathrm {Im}(a)) - \phi (c,b,a)^2 \bigg ),\) 
